In this paper we develop a cost model for the single-model stochastic assembly line balancing problem for the objective of minimizing the total labour cost (dicated by the number of stations on the line) and the expected incompletion cost arising from tasks not completed within the prescribed cycle time. Its use is demonstrated in a dynamic programming procedure which is implemented using a bounding strategy to curtail storage and computational requirements. The solutions obtained are compared with those obtained using the procedure of Kottas and Lau (1973, 1981).